We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called r-ELSV formula, as well as its orbifold generalization, the so-called qr-ELSV formula.
Dunin-Barkowski, P., Kramer, R., Popolitov, A., Shadrin, S. (2023). Loop equations and a proof of Zvonkine’s qr-ELSV formula. ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE, 56(4), 1199-1229 [10.24033/asens.2553].
Loop equations and a proof of Zvonkine’s qr-ELSV formula
Kramer R.;
2023
Abstract
We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called r-ELSV formula, as well as its orbifold generalization, the so-called qr-ELSV formula.
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